Algebra Examples

$(17 \sqrt{2 z^{2}}) (4 \sqrt{12 z^{2}})$

Step 1

Reorder $2$ and $z^{2}$ .

$17 \sqrt{z^{2} \cdot 2} (4 \sqrt{12 z^{2}})$

Step 2

Pull terms out from under the radical.

$17 (z \sqrt{2}) (4 \sqrt{12 z^{2}})$

Step 3

Rewrite $12 z^{2}$ as ${(2 z)}^{2} \cdot 3$ .

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Step 3.1

Factor $4$ out of $12$ .

$17 z \sqrt{2} (4 \sqrt{4 (3) z^{2}})$

Step 3.2

Rewrite $4$ as $2^{2}$ .

$17 z \sqrt{2} (4 \sqrt{2^{2} \cdot 3 z^{2}})$

Step 3.3

Move $3$ .

$17 z \sqrt{2} (4 \sqrt{2^{2} z^{2} \cdot 3})$

Step 3.4

Rewrite $2^{2} z^{2}$ as ${(2 z)}^{2}$ .

$17 z \sqrt{2} (4 \sqrt{{(2 z)}^{2} \cdot 3})$

$17 z \sqrt{2} (4 \sqrt{{(2 z)}^{2} \cdot 3})$

Step 4

Pull terms out from under the radical.

$17 z \sqrt{2} (4 (2 z \sqrt{3}))$

Step 5

Multiply $z$ by $z$ by adding the exponents.

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Step 5.1

Move $z$ .

$17 (z \cdot z) \sqrt{2} (4 (2 \sqrt{3}))$

Step 5.2

Multiply $z$ by $z$ .

$17 z^{2} \sqrt{2} (4 (2 \sqrt{3}))$

$17 z^{2} \sqrt{2} (4 (2 \sqrt{3}))$

Step 6

Multiply $2$ by $4$ .

$17 z^{2} \sqrt{2} (8 \sqrt{3})$

Step 7

Multiply $17 z^{2} \sqrt{2} (8 \sqrt{3})$ .

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Step 7.1

Multiply $8$ by $17$ .

$136 z^{2} \sqrt{2} \sqrt{3}$

Step 7.2

Combine using the product rule for radicals.

$136 z^{2} \sqrt{3 \cdot 2}$

Step 7.3

Multiply $3$ by $2$ .

$136 z^{2} \sqrt{6}$

$136 z^{2} \sqrt{6}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$